Optimal design using implicitly given function sets

A system equation with certain properties describes implicitly function sets as the basis for an optimal design of a digital circuit. A necessary condition for the realization of a digital circuit is that the associated system equation is resolvable. This paper shows how the resolvability of the system equation can be checked and how the explicit description of the circuit functions can be calculated. Basic knowledge of the Boolean differential calculus is used to point out the theory of resolvability. This theory and its transformation into efficient algorithms are demonstrated by an example (the optimal design of a non-deterministic finite state machine).